Homogeneous Einstein Metrics on Generalized Flag Manifolds with G(2)-type T-Roots

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Authors	CHRYSIKOS Ioannis ARVANITOYEORGOS Andreas SAKANE Yusuke
Year of publication	2013
Type	Article in Proceedings
Conference	Prospects of Differential Geometry and Its Related Fields Proceedings of the 3rd International Colloquium on Differential Geometry and Its Related Fields
MU Faculty or unit	Faculty of Science
Citation
Web	https://www.worldscientific.com/doi/abs/10.1142/9789814541817_0002
Doi	http://dx.doi.org/10.1142/9789814541817_0002
Field	General mathematics
Keywords	Homogeneous Einstein metric Generalized flag manifold Riemannian submersion Grobner basis
Description	We construct the Einstein equation for an invariant Riemannian metric on generalized flag manifolds G/K with G2-type t-roots. By computing a Gr¨obner basis for a system of polynomials on six variables, we prove that such a generalized flag manifold G/K, which is not the full flag manifold G2/T, admits exactly one invariant Kahler Einstein metric and six non Kahler invariant Einstein metrics up to isometry and scalar.
Related projects:	Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku